Can x/0 be divided out

  1. ShawnD

    ShawnD 986
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    Say I had an expression that went like this

    [tex]\frac{ 5 \frac{x}{0} }{3 \frac{x}{0} }[/tex]

    Can I divide those [itex]\frac{x}{0}[/itex] terms or do they make the expression undefined?
     
  2. jcsd
  3. chroot

    chroot 10,426
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    Nope, you can't divide them out. The entire expression is indeterminate (NOT undefined).

    - Warren
     
  4. matt grime

    matt grime 9,396
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    I wouldn't say you can't divide them out so much as what you wrote is just plain wrong, being polite about it - the symbols make no sense as written.
     
  5. chroot

    chroot 10,426
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    I think he means

    [tex]\frac{ 5 \cdot \frac{x}{0} }{3 \cdot \frac{x}{0} }[/tex]

    to be read "5 times x over 0...", not "5 and x zeroths..."

    - Warren
     
  6. matt grime

    matt grime 9,396
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    But is still makes no sense. x/0 is not a well-defined symbol in the real number system that one can manipulate like this.
     
  7. I think that was part of his question.
     
  8. 1/0.1 is tha same as 1*10
    1/0.01 is tha same as 1*100
    1/0.001 is tha same as 1*1000
    and so on ...

    1/0 is the same as 1*oo and in both cases we are no longer in a finite system.

    oo is a general notation for infinity therefore 1/0 is also a general notation for infinity.

    Please look at: http://mathworld.wolfram.com/Infinity.html
     
  9. Zurtex

    Zurtex 1,123
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    Note for others, in the link given it goes points out:

    "Informally,[itex]1 / \infty = 0[/tex] , a statement which can be made rigorous using the limit concept"

    You can't just say:

    [tex]\frac{1}{\infty} = 0[/tex]

    or any manipulation of that as and think it is mathematically true.
     
  10. Hurkyl

    Hurkyl 16,090
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    Discussion over the foundations of limits split to new thread. Please stop hijacking threads.
     
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